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Competitive Equilibrium

Summary: In this experiment, students participate as buyers and sellers in a competitive market. By participating in this game, students get a first-hand glimpse of the invisible hand, and how a market made up of buyers and sellers acting to maximize their own profits can generate competetitive outcomes. In addition, the experiment allows students to observe how well markets can react to changing supply and/or demand conditions.

Motivation: Students sometimes doubt the textbook presentation of the supply or demand model, or simply memorize that equilibrium occurs whenever two lines intersect one another. Moreover, when the emphasis is on theory and graphs, students may easily lose track of the fact that the supply and demand model should be able to predict how prices and quantities actually react to changing market conditions. By participating in this market game as buyers and sellers, students observe that the competitive outcome is quite robust, and that market outcomes frequently track the equilibrium prediction even when demand or supply is changing.

Concepts Covered:

  1. How induced values may be used to generate market supply and demand curves.
  2. Determining equilibrium price and quantity with induced values.
  3. The competitive model's power to describe behavior in a market.
  4. The role of market institutions in the competitive model.
Time Required: This experiment and associated discussion can be conducted in one 75-minute class. Experiment instructions take about 15 minutes, conducting a computerized experiment will take about 25 minutes, and discussion can be completed in about 25. If your class meets for 50 minutes, you should consider having students read the instructions before coming to class. Alternatively, you can have students participate in this experiment online outside of classtime, then discuss the market in the next class period.

Computerized Market Experiment

Materials: No materials are required for using the computerized market experiment other than EconPort software.

This configuration includes student instructions, but if you want students to read instructions earlier than immediately before playing the game, then they can read the following instructions:

student instructions

Considerations:
  1. This experiment can be conducted with any size class. The configuration is set up for a maximum of 100 people. If your class is larger than this or you prefer to run smaller markets, you can simply conduct multiple markets within one class.

  2. If you want to use the "Demand and Supply" module, you should complete that exercise before doing this one. We typically conduct this exercise after covering demand and supply, but before lecturing on equilibrium; however, if the timing works better for you, this exercise is still quite valuable when it follows a lecture on equilibrium.

  3. This experiment works fine with hypothetical earnings, or you can randomly select one student to pay a fraction of earnings.
Overview:

In the "Demand and Supply" module we used a real good (candy) to obtain students' willingess to pay (MB) and willingness to accept (MC). In that experiment, costs and values were "homegrown" - they were the stated values given by students. In contrast, the demand and supply curves used in this module are generated using "induced values" - we don't specify the good being bought and sold; instead, we tell buyers in the market how much the good is worth to them and tell sellers in the market their costs of production. In other words: instead of the students determining their own costs and values, we explicitly tell them what they are. In this way, we are able to control the demand and supply curves used in the game, and to generate changes in supply and demand if desired.

The induced values work by generating (hypothetical) earnings for subjects based on the cost and value information provided to them. Buyers are told that their (hypothetical) profit is equal to the induced value minus the price they agree to pay for the good. This profit represents consumer surplus. For example, a buyer might be told that their value is $10; if this buyer finds a seller willing to sell at a price of $8, this buyer receives a profit of $2 - he or she paid $2 less than his value of the good. Similarly, sellers are told that their (hypothetical) profit is equal to the price they agree to sell at minus the induced cost. This profit represents producer surplus - the gains from trade over and above marginal cost. In the lecture section of this module we present suggestions for explaining to students how these induced values generate market supply and demand curves.

Additional Instructions for the Professor
  1. In the first two or three rounds of this experiment, there is typically a great deal of variation in market prices as students learn about how to make bids and offers and how to accept bids and offers. However, prices typically converge to the competitive outcome after five or six trading rounds.

  2. If you are running short on time, it is possible to conduct this experiment for only six or seven rounds under the initial supply and demand conditions. However, our recommended setup is to conduct seven rounds under the initial setup and then implement a demand shift (reduction) after round 7, then conduct 7 more rounds under the new conditions. We find that students have more faith in the competitive model when they see how it tracks a changing equilibrium prediction.

  3. If you are running short on time, a better way to save time is to assign the instructions to students outside of class so that you can immediately start the experiment when class begins.

  4. For added "drama" you can put the equilibrium price and quantity on an index card in a sealed envelope before class. Show students the sealed envelope before the experiment begins and tell them that it contains your prediction as to what price and quantity traded will eventually happen in the market. Put it in a public place and tell students that you will open it at the end of the experiment.

Lecture

Once students have participated in the experiment, you should get them involved in the class discussion as much as possible. Participating in the experiment will have given them an opportunity to really think about the public goods problem (though this term has not yet been introduced) and therefore the role of the discussion period should be to help them summarize what they have learned and put it into economic terms. To facilitate this, the "lecture" is presented as a series of questions that you can ask your students, with suggestions for summarizing their answers and leading them through the material associated with the public goods problem.

Introduction

Some of the material in this lecture assumes that you have also used the Demand and Supply module. If you choose to skip that module and start with this experiment, you can omit those portions that compare induced values to homegrown values.

A good way to start the discussion is to write the buyers' values and sellers' costs on the board; it is best if you do NOT initially put them in order (from high to low for buyers' values, and from low to high for sellers' costs). The idea is to get students to think about these costs and values and what they mean, and then to think about putting them in order. For example:

Values: 10, 8, 6, 9, 5, 8, 4, 7, 7, 6
Costs: 8, 2, 5, 4, 6, 7, 3, 5, 6, 2

Tell students that these were the costs and values that were used in this market.

Next, ask a student if her or she had any idea of what the other students' costs and values were in this experiment. Almost all students will answer that they were not able to infer this information from the market. After this, ask a student to explain how they were able to determine what price to accept if they didn't know anything about others' costs or values. Most students will answer that they were just trying to obtain the most profit that they could, or that they observed the prices that had already been agreed on in the market and used that to determine what was a reasonable price. Others will point out that they tried for a price that led to a very high profit early in the round, but eventually (as it got close to the end of the period) they would accept any price that would lead to a profit, even if it was small.

After this, ask students to look at the values and costs and tell you how you might look at these numbers to determine what price you should "expect" in the market. Answers to this question vary a lot - the point here is not that students get the right answer but to start them along the lines of thinking about how the theoretical prediction might be obtained. Only very rarely - even in upper-level or graduate classes - does a student quickly determine how the actual prediction is obtained.

Discussion Points

After students have had a few minutes to thin about this and discuss this, you can lead them by asking them a series of pointed questions using the specific costs and values used in the experiment. For example, using the costs and values above:

  1. At a price of $9, how many buyers would be willing to purchase this good? (Assume that anyone would buy as long as they do not make a loss - in other words, a person will buy even if they earn zero profit.) It typically helps if you remind students (by writing on the board) that a buyer's profit is calculated as: value - price, so one will buy as long as their value is at least as great as the price. The answer to this question is that 2 buyers would purchase : the buyers with values of $9 and $10. All other buyers have values less than $9, and so they would lose money if they were to buy at this price.

  2. At a price of $9, how many sellers would be willing to sell this good? (Assume that anyone would sell as long as they do not make a loss - in other words, a person will sell even if they earn zero profit.) It typically helps if you remind students (by writing on the board) that a seller's profit is calculated as: price - cost, so one will sell as long as their cost is no greater than the price. The answer to this question is that all 10 sellers would be willing to sell because all have a cost of less than $9.

  3. If there are 10 sellers who want to sell at a price of $9 and only 2 buyers who want to buy at a price of $9, what would you expect to happen? Most students will understand that sellers will be willing to reduce their price in order to attract more buyers.

  4. Let's look at another example. At a price of $4, how many buyers would be willing to purchase this good? (We will still assume that anyone would buy as long as they do not make a loss - in other words, a person will buy even if they earn zero profit.) All 10 buyers would be willing to purchase because all have a value that is $4 or higher.

  5. At a price of $4, how many sellers would be willing to sell this good? (We still assume that anyone would sell as long as they do not make a loss - in other words, a person will sell even if they earn zero profit.) Only 4 sellers would be willing to sell at this price: two sellers with a cost of $2, one seller with a cost of $3, and one seller with a cost of $4.

  6. If there are 10 buyers who want to buy at a price of $4 and only 4 sellers who want to sell at a price of $4, what would you expect to happen? Most students will realize that either sellers will demand a higher price or that buyers will start to compete with one another and offer higher prices.

  7. So, we've decided that a price of $9 can't last because sellers will reduce their price to try to attract more buyers, and a price of $4 won't last because buyers will offer to pay more to find a seller, so how do we figure out what price would work in this market? At this point, some students will quickly realize that the only price that will work is when there are an equal number of buyers and sellers who are willing to trade at that price. If your students don't, you can ask some more leadiing questions: Is there something special about the $9 price that causes prices to come down from this point? It's just that there aren't many buyers who are willing to buy and a lot of sellers who are willing to sell. What if there were 6 sellers who wanted to sell and only 4 buyers who wanted to buy? The other two sellers would still want to reduce their price. What if the situation was the opposite, and there were 6 buyers who wanted to buy and only 4 sellers who wanted to sell? The two buyers who were left out might try to offer a higher price so that they can buy.

  8. At this point, you can summarize the discussion so far: when there is a different number of buyers and sellers who want to trade at a given price, those who are left out of the market change their bid or offer so that they can try to make a trade.

  9. When will this NOT occur? When there is the same number of buyers and sellers who want to trade.

  10. If we wanted to determine what this price would be in our market, is there an easier way to look at these costs and values in order to determine how many people would be willing to buy and sell at various prices? You may get a variety of answers to this question, but eventually students will hit upon the idea that if you put them in order (for example, from low to high) it will be easier to tell this information.

  11. Let's put the buyers' values in order first. Who is most likely to make a purchase in this market - the buyer with a value of $10 or the buyer with a value of $4? There are a lot of prices at which the buyer with a $10 value will buy, when the buyer with a $4 value won't (for example, if the price is $7 or $8). So, the buyers with the highest values will be the most likely to buy. So, when we order our buyers, we should start with them:

  12. Values (ordered highest to lowest): 10, 9, 8, 8, 7, 7, 6, 6, 5, 4

  13. Looking at this, how many buyers would be willing to purchase at a price of $10? 1 buyer. (Write this, and all the rest on the board; putting it into a table may help). At a price of $9? 2 buyers (the buyers with values of $10 and $9). At a price of $8? 4 buyers (the buyers with values $8 and higher). At a price of $7? 6 buyers. At a price of $6? 8 buyers. At a price of $5? 9 buyers. At a price of $4? 10 buyers.

  14. Next, let's put the sellers' costs in order. Who is most likely to make a sale in this market - the seller with a cost of $8 or the seller with a cost of $2? There are a lot of prices at which the seller with a $2 cost will sell, when the seller with an $8 cost won't (for example, if the price is $5 or $6). So, the sellers with the lowest costs will be the most likely to sell. So, when we order our sellers, we should start with them:

  15. Costs (ordered lowest to highest): 2, 2, 3, 4, 5, 5, 6, 6, 7, 8

  16. Looking at this, how many sellers would be willing to sell at a price of $2? 2 sellers. (Write this, and all the rest on the board in a table; if you like, you can put it in the same table that you used for buyers, but start at the bottom, adding rows for prices of $2 and $3.) At a price of $3? 3 sellers (the two buyers with a cost of $2 and one seller with a cost of $3). At a price of $4? 4 sellers. At a price of $5? 6 sellers. At a price of $6? 8 sellers. At price of $7? 9 sellers. At price of $8? 10 sellers. At a price of $9? 10 sellers. At a price of $10? 10 sellers.

  17. Looking at these numbers, is there any price where the number of buyers who are willing to buy is the same as the number of sellers who are willing to sell? Yes - when the price is $6, there are 8 buyers willing to buy and also 8 sellers willing to sell.
Point out to students that this is what we call the equilibrium price and quantity in the market; equilibrium is a state of balance, where things come to rest. In microeconomics, we say a market is in equilibrium when the number of people willing to buy is exactly equal to the number people are willing to sell.

Graphs

At this point, you can turn to presenting this information graphically. If you have already conducted the Demand and Supply module with your class, this will be relatively easy; in that module you graphed demand and supply functions that came from self-reported willingness to pay and willingness to accept for candy. In this case, you are graphing supply and demand functions that come from induced values. Even if you have not covered this module with your class, the lecture suggestions contained in this module may be helpful as you present this to your students. In particular, this module describes the type of step-function that comes out of a market such as this one with discrete units.

Demand and Supply Teaching Module

On the board, you should draw the information contained in the table, first for market demand (buyers' values) and then for market supply (sellers' costs). Do this step-by-step. For example, when graphing buyers' demand curve, start with a price of $11 and show that no buyer would be willing to purchase. This would also be true at $10.75, $10.50, etc. until the price hits $10. At this point, there is one buyer that is willing to purchase at this price. So there is a horizontal line that can be drawn at a price of $10 that goes out to a point of 1 unit. Next, ask about how many buyers would purchase at a price of $9.50? The answer is still 1 buyer - the buyer with a $10 value, since the buyer with a $9 value would lose $0.50 if he or she bought at $9.50. Show on your graph another point, with one unit that would be purchased at a price of $9.50. It doesn't hurt at first to be very explicit about this: you might want to draw a third point at a price of $9.25, when there is still only 1 unit that would be purchased, and another at $9.10. Next ask how many units would be purchased at a price of $9? As students have already seen, two people would be willing to buy at this price, and so now you can draw another discrete step at $9.

This process should be continued for each step of the demand curve. Point out to students that not all steps are the same size; for example, when the price falls from $9 to $8, the number of willing buyers increases from 2 to 4, so the step at a price of $8 is twice as long as that at $9 or $10. After this, approach graphing the supply curve in the same manner. Students may then observe that the two curves intersect at a price of $6, with 8 units traded.

At this point, you can turn to the results from the classroom experiment. Remind students that you said that you could predict the outcome: open the envelope and show that the predicted price in the market is $6. Next, you can use the Econport software to show students the actual prices at which units traded in the market.

(More details to come)

Start by discussing the first 7 rounds, and then tell students that there was a shift in Demand after round 7; the values used in the market were reduced, and so there was a new equilibrium prediction. You can then show the results from the remaining rounds to demonstrate how the actual trading prices tracked this changing equilibrium.

 
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